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CAIE A Level Mathematics 9709

Complex numbers questions

Exam-style questions on Complex numbers, ordered from foundation to challenge. Pick one, write your answer the way you would in the exam, and it comes back marked against the mark scheme, point by point.

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Written by Markquill to follow the Cambridge International syllabus. Markquill is independent and is not affiliated with or endorsed by Cambridge International.

  1. 1 markFoundationLet z1 = -3 - 7i and z2 = -7 - 6i. Find the real part of z1 - z2.
  2. 1 markFoundationFind z ^2 where z = -9 - 9i.
  3. 1 markFoundationLet z1 = 2 + i and z2 = 1 + i. Find the imaginary part of z1 + z2.
  4. 1 markFoundationLet z1 = 0 - 8i and z2 = 8 + 4i. Find the imaginary part of z1 - z2.
  5. 2 marksFoundationFind the modulus of z = 15 + 20i.
  6. 1 markFoundationLet z1 = -9 - 2i and z2 = 9 + 4i. Find the real part of z1 + z2.
  7. 2 marksFoundationGiven the complex number z = -4 - 3i , find its modulus z .
  8. 2 marksFoundationTwo complex numbers are given in polar form: z1 = 3 cis (0.785398 ) z2 = 3 cis (0 ) Find the modulus of the product z1 × z2.
  9. 2 marksFoundationFind the modulus of z = 35 + 12i.
  10. 2 marksStandardLet z1 = 0 - 5i and z2 = -4 - i. Find the real part of z1 z2.
  11. 2 marksStandardFor z = 5 + 7i, find the value of zbarz.
  12. 2 marksStandardFor z = -5 + i, find the real part of z^2.
  13. 2 marksStandardLet z1 = -2 - 2i and z2 = 2 - 4i. Find the imaginary part of z1 z2.
  14. 2 marksStandardFor z = -1 + 5i, find the imaginary part of z^2.